The optimization procedure is iterated until convergence, that is when the difference between the likelihood function evaluated at two consecutive iterations is smaller than \(10^{-5}\) . We initialize the EM algorithm by providing the univariate parameter estimates of [1]} on each asset, while the initial value for the correlation matrix \(\Psi \)  in (REF ) is calibrated using the empirical correlation matrix of the data. We fit the univariate models following the estimation procedure in [2]} and [1]}. In addition, we also consider a multiple random starts strategy with 100 different starting points to better explore the parameter space, and retain the solution corresponding to the maximum likelihood value. This strategy would prevent convergence issues and avoid the algorithm to be trapped at some local maxima. From an algorithmic point of view, the EM method exploits the Nelder-Mead and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization routines to obtain the blackupdated estimates of \(\beta \)  and \(\gamma \) , meanwhile it uses (REF ) to compute the blackupdated estimate of \(\tilde{\Sigma }\) .
